Priority queues in C++ are data structures that allow you to efficiently retrieve the element with the highest (or lowest) priority. The standard library provides a priority_queue container adapter that is built on top of a heap. By default, it implements a max-heap, where the largest element has the highest priority.

Here's a quick overview of how to use std::priority_queue:

Basic Usage

1. Include the necessary headers:

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   #include 
   #include 
   

2. Create a priority_queue:

   By default, it uses a max-heap (largest element has the highest priority).

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   std::priority_queue<int> pq;
   

3. Add elements to the priority queue:

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   pq.push(10);
   pq.push(20);
   pq.push(15);
   

4. Access the top element (highest priority):

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   std::cout << "Top element: " << pq.top() << std::endl;  // Outputs 20
   

5. Remove the top element:

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   pq.pop();
   

6. Check if the priority queue is empty:

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   if (pq.empty()) {
       std::cout << "Priority queue is empty." << std::endl;
   }
   

Custom Comparator

You can also use a custom comparator to change the behavior of the priority queue. For example, to create a min-heap (where the smallest element has the highest priority), you can use the following approach:

1. Include the necessary headers:

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   #include 
   #include 
   #include 
   

2. Define a custom comparator:

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   struct Compare {
       bool operator()(int a, int b) {
           return a > b;  // Min-heap (smallest element has the highest priority)
       }
   };
   

3. Create a priority queue with the custom comparator:

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   std::priority_queue<int, std::vector<int>, Compare> pq;
   

4. Add elements and use the priority queue as before:

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   pq.push(10);
   pq.push(20);
   pq.push(15);
   std::cout << "Top element: " << pq.top() << std::endl;  // Outputs 10
   

Example Code

Here's a complete example demonstrating both the default max-heap and a custom min-heap:

cpp
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#include 
#include 
#include 

// Custom comparator for a min-heap
struct Compare {
    bool operator()(int a, int b) {
        return a > b;  // Min-heap
    }
};

int main() {
    // Default max-heap
    std::priority_queue<int> maxHeap;
    maxHeap.push(10);
    maxHeap.push(20);
    maxHeap.push(15);

    std::cout << "Max-Heap:" << std::endl;
    while (!maxHeap.empty()) {
        std::cout << maxHeap.top() << " ";
        maxHeap.pop();
    }
    std::cout << std::endl;

    // Custom min-heap
    std::priority_queue<int, std::vector<int>, Compare> minHeap;
    minHeap.push(10);
    minHeap.push(20);
    minHeap.push(15);

    std::cout << "Min-Heap:" << std::endl;
    while (!minHeap.empty()) {
        std::cout << minHeap.top() << " ";
        minHeap.pop();
    }
    std::cout << std::endl;

    return 0;
}

This code will output:

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Max-Heap:
20 15 10
Min-Heap:
10 15 20

Feel free to adjust the example based on your specific needs!